A manufacturer has a monthly fixed cost of $100,000 and a production cost of $16 for each unit produced. The product sells for $20/unit.(c) What is the profit function, P(x)?

Question

(d) Compute the profit (loss) corresponding to production levels of 12,000 and 47,000 units. 

P(12,000) units	$
P(47,000) units	$

Answer 1

Profit = Revenue - Cost

From the problem, we can form the following equations.

R=20x

C=100000+16x

Now, plug these into the main equation, P=R-C

P=20x-(100000+16x) Distributive property to clear parenthesis

P=20x-100000-16x Simplify by combining like terms

P=4x-100000

Now to plug in the values

P(12000) = 4(12000)-100000

=48000-100000 = -$52,000 loss

P(47000) = 4(47000)-100000

=188000-100000 = $88,000 profit